Most cheap gennys provide a really dirty wave form, and can have peaks way outside the 240v area. I have seen chargers damaged by such use, and some battery charger makers will not repair them if they know they have been used on inadequate units. Most cheap gennys are alwo way under rated and cannot deliver the expected output, which gives and even worse waveform. Inverter gennys should be OK (pure sine wave is needed) but many are just too small. It must be able to deliver at least 10amp continuously so a 3kw continuous would be minimim. Same thing if trying to charge from a battery pack and inverter. It must be a pure sine wave. Cheap ones are a modified sine which is a step / square wave and this is no good.
Large industrial generators are not such a problem and are generally a good clean waveform. (Ie the ones that are about the size of a small car .)

This one is 7.5 kilos, does 10w continuous. Could this be used to give the Twizy a boost charge even if not full? They do huge ones up to 40 kilos, still a small passenger weight though.

The solar mention is only that you can buy a panel to recharge the brick

PRODUCT DESCRIPTION

The combination of the Goal Zero Yeti 400 lithium Portable Power Station and the Goal Zero Boulder 100 Solar Panel is the perfect, portable combination for different situations. Ideal for camping, in a garden shed or as an emergency facility. The Yeti 400 Lithium has a capacity of 428 Wh and can supply devices up to 300 watts of energy. The Boulder 100 solar panel fully charges the Yeti Portable Power Station in 6 - 7 hours.